# Tag Info

### What value is there in requiring students to answer word problems in complete sentences?

Yes, there is mathematical pedagogical value in the usage of complete sentences - but this does not only refer to "answers" and not only to "word problems", but to all parts of the ...

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I'm confused. Are you really going to try to make this sort of distinction when teaching geometric figures to students "around 9-13 years old"? Students that age (and engineers my age -- ...

### What value is there in requiring students to answer word problems in complete sentences?

I do think there is value in expecting students to give answers in correct English. It will certainly help when they start to face longer and less structured questions. However, the example you give ...

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

One encounters exactly the same issue teaching multivariable calculus when one treats integrals over three-dimensional regions and integrals over the surfaces that are their boundaries. In particular ...

### What value is there in requiring students to answer word problems in complete sentences?

An example of a problem where phrasing the answer as a sentence might prevent mistakes and encourage understanding is: Alice goes to the store with \$2.00. A gumball costs \$0.80. How many gumballs ...

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I think the distinction you are raising is not natural to students at this age. I teach undergraduates and graduate students, not elementary schoolers, but I find that it is not natural for ...

### Can we save the word "unique"?

I don't see this as a major issue, nor do I believe that the word "unique" is in any particular need of saving. There are a large number of terms in mathematics which correspond to ...

### Examples of Mathematical Slang

One of the most colorful names I have heard is the Chicken Mc Nugget theorem: for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ ...

### Can students tell the difference between the "definition if" and the "theorem if"?

Not formal research, but some decades of experience teaching both undergrad and graduate level courses, and "editing" PhD theses and such: It appears that even many serious professional ...

### What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

In my experience with remedial-level community-college students (USA), it is simply never the case that the units are trivially "clear from context". I can easily see some of my former ...

### What is it called when terms disappear when reducing fractions?

So German "$b$ kürzt sich weg" becomes in English "$b$ cancels out". We may also say "$b$ is eliminated".

### How to reduce ambiguity in the following question?

The ambiguous answer is relatively correct (actually you need to know how old they are at the start of the problem). But each fission is an individual splitting, not a generation. Perhaps this: A ...

### Examples of Mathematical Slang

How about the shoelace formula for the area of an arbitrary simple polygon?                     (Image from Wikipedia.) The formula computes the ...

### Examples of Mathematical Slang

In Central Mexico, the expression \begin{equation} x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{equation} that solves quadratic equations of the form $ax^2 + bx + c = 0$ is called "fórmula del ...

### What's the common word for equations and inequalities?

My phrase has always been math "statement". Equations and inequalities clearly assert/state a relationship between two or more things. My go-to direction using this would be something like: &...

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Educator here who has worked with many students in the aforementioned age range (9-13) on triangles and squares. In my experience, it has never come up that a confusion between the boundary and the ...

### What value is there in requiring students to answer word problems in complete sentences?

Jochen's answer is very good. To add to it, here's the reasoning I was given as a student: answering in full sentences makes students think about the answer in different psychological context. This ...

### Is 'For all $x$' an abuse of language in math?

No, there is no abuse of language here. $x$ and $y$ are placeholders that stand for individual numbers, and your second suggestion captures this: For each number we can insert in place of $x$ and $y$, ...

### Examples of Mathematical Slang

In Russian, the Squeeze Theorem (a.k.a. The Pinching Theorem) is called "Теорема о двух милиционерах" — "Two Policemen Theorem". The idea is that if two policemen are holding a criminal between ...

### Examples of Mathematical Slang

I often refer to the identities $(AB)^{-1} = B^{-1}A^{-1}$ or $(AB)^T = B^TA^T$ as the socks-shoes identity. I'm not sure how wide-spread this is, I certainly did not invent it and I'm pretty sure I'...
Accepted

### Examples of Mathematical Slang

My elementary students always wanted to know the name of the symbol shown here: We called it the division house as did many of my colleagues, but my students wanted a mathematical name. We therefore ...
Accepted

### Phrasing the Van Hiele levels in student-friendly language

The argument has been made that this is sort of a misappropriation of the terms, because the levels are meant to define levels of understanding rather than levels of detail. I'm assuming what you're ...
To my mind the defintion "Every x has a unique f(x)" of one-to-one is problematic because "has a unique" is neither clear English nor precise. The definition is usually stated as "$f(x) = f(y)$ ...